I have quite a large amount downloaded but my favourite has to be Tilt to Live. It was recommended by a friend and I dismissed it at first but when I picked it up during a sale I fell in love with it. It is simple yet highly addictive and it's the sort of game which makes you think "just one more try" everytime you lose. It isn't for everyone but there is four modes (a forth is available to purchase which is my second favourite mode after the classic one) available and if you are the sort of person that likes to beat high scores it is for you.
Angry Birds is another one of my favourites but I impulsively try to get three stars in each level and after awhile it can become very frustrating so it's better off played in short does.
Zenbound 2 (I haven't played the first) is a very good puzzle game that can be quite challenging.
As Tomasu said, Infinity Blade is very good. It has the most amazing graphics I've seen on the iPhone and I highly recommend it but, it's worth noting that some people find the gameplay boring so you may want to read up on how it handles. It may be important to know that it is a very big download for an iPhone game totalling (I think) roughly 496MB.
Osmosis is also a game I really love but it is hard to explain. Very basically, you are a small orb that absorbs other orbs to become bigger and you must avoid orbs bigger than you (although keep in mind that that is a very simple explanation. It is very relaxing but I don't play it as much as Tilt to Live or Angry Birds.
Peggle is another one I highly recommend. If you aren't familiar with it, you launch a ball and try to hit all the orange pegs. There are lots of blue pegs which add points and green pegs which use your character's special ability. It's quite addictive and I had a hard time putting it down once I bought it. You would however have to enjoy trying to beat your own highscores if you want much of a reason to replay it but there are enough levels to keep you entertained for a good while anyway.
Dead Spae is one I bought last week and although I'm only about two hours in I'm highly impressed. The graphics are good, almost upto Infinity Blade in my opinion, the controls are superb, the story is good and it plays just like the console games do. Really, if you like either Dead Space 1 or Dead Space 2 you will like this. It is however expensive for an iPhone game and since I've not yet finished it I don't know how long it is or how much replayability there I'd but if it is like the console ones you should be able to replay it with all your equipment and nodes.
Plants Versus Zombies is a good base defense game and there really isn't that much more I can say about it tbh.
Some other notable mentions go to NOVA, NOVA 2, Doodle Jump, Cut the Rope (which is enjoyable if not a bit too easy), Predators, Mirror's Edge, Silverfish, Death Worm, Deviant Pixel and Trainyard.
I do want to recommend another game which is called Sandslides. It's definitely not for everyone but I'm finding it very enjoyable so far (I've only played about an hours worth of it) and It was free when I downloaded it (maybe it still is). I don't want to put it with the first list of games as I haven't played it anywhere near as long as them and it may get boring after a few more hours.
I recommend checking out a website called App Advice (I can't remember the exact website address since I use the iPhone app. but it is very good providing a daily list of apps. that have gone free, weekly (mostly) lists of apps. on sale, reviews and news in general about Apple products (although they are almost completely focused on the iPhone, iPod Touch and the iPad so don't expect all the latest information on Macs)
I hope that helps.